可数正规子群的商是超有限的

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2023-07-02 DOI:10.4171/ggd/719

Joshua Frisch, Forte Shinko

引用次数: 0

摘要

我们证明了对于任何波兰群G和任何可数正规子群Γ/G，陪集等价关系G/Γ是超有限Borel等价关系。特别地，任何可数群的外自同构群都是超有限的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Quotients by countable normal subgroups are hyperfinite

We show that for any Polish group G and any countable normal subgroup Γ/G, the coset equivalence relation G/Γ is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any countable group is hyperfinite.

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.